What is the answer for this aptitude question?

Question

If $13!/2^x$ is an integer, which of the following represents all possible values of $x$?

a) $0 \le x \le 10$

b) $0 < x < 9$

c) $0 \le x < 10$

d) $1 \le x \le 10$

e) $1 < x < 10$

The book says d). But why can't it be a)? Since $13!/2^0$ is also an integer, right?

Answer 1

Yes you are right and the book is wrong.

13! has six factors of two, three factors of four, and one factor of eight, so $13!/2^{10}$ is an integer, and $13!/1=13!/2^0$ is an integer.

Answer 2

ALL possible answers. Any x: 0 < x < 1 will not give you an integer, so even though 0 works, you have to throw out that part of the interval.